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A241243 Decimal representation of sin(Pi/17).

%I A241243 #47 Aug 31 2025 11:24:55
%S A241243 1,8,3,7,4,9,5,1,7,8,1,6,5,7,0,3,3,1,5,7,4,4,0,8,8,3,9,6,2,0,7,2,7,5,
%T A241243 8,2,4,8,9,1,3,8,5,2,3,8,4,4,4,9,9,4,0,5,8,5,0,6,5,0,8,5,7,7,4,8,9,1,
%U A241243 4,9,2,8,2,5,3,0,5,0,1,7,3,0,3,0,6,0,1,1,9,5,1,2,1,0,7,3,0,4,8,5,9,2,9,6,7,9,7,6,3,4,0,0,2,9,7,4,9,1,6,9
%N A241243 Decimal representation of sin(Pi/17).
%D A241243 Saul Stahl, "Geometry From Euclid To Knots" Chapter 4.3, 'Regular Polygons', Courier - Dover Publications, NJ, 2009, pp. 153-154.
%H A241243 Wikipedia, <a href="http://en.wikipedia.org/wiki/Constructible_polygon">Constructible polygon</a>
%H A241243 <a href="/index/Al#algebraic_16">Index entries for algebraic numbers, degree 16</a>
%F A241243 Equals 1/4 sqrt(8 - sqrt(2*(15 + sqrt(17) - sqrt(2*(17 - sqrt(17))) + sqrt(2*(34 + 6 sqrt(17) + sqrt(2*(17 - sqrt(17))) - sqrt(34*(17 - sqrt(17))) + 8*sqrt(2*(17 + sqrt(17)))))))). - _Robert G. Wilson v_, Aug 14 2014
%F A241243 The minimal polynomial is 65536x^16 - 278528x^14 + 487424x^12 - 452608x^10 + 2398360x^8 - 71808 x^6 + 11424x^4 - 816x^2 + 17. - _Robert G. Wilson v_, Aug 14 2014
%F A241243 This^2 + A210649^2 = 1. - _R. J. Mathar_, Aug 31 2025
%e A241243 0.18374951781657033157440883962072758248913852384449940585065085774891492825305...
%p A241243 Digits:=100: evalf(sin(Pi/17)); # _Wesley Ivan Hurt_, Aug 15 2014
%t A241243 RealDigits[ Sin[ Pi/17], 10, 111][[1]] (* _Robert G. Wilson v_, Aug 14 2014 *)
%t A241243 RealDigits[Root[17 - 816 x^2 + 11424 x^4 - 71808 x^6 + 239360 x^8 -
%t A241243   452608 x^10 + 487424 x^12 - 278528 x^14 + 65536 x^16, 9],10,105][[1]] (* _Artur Jasinski_, Aug 04 2025 *)
%K A241243 nonn,cons,changed
%O A241243 0,2
%A A241243 _Zak Seidov_, Apr 18 2014
%E A241243 Offset corrected by _Amiram Eldar_, Aug 04 2025